The equation gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds).
-$\mathrm { s } = 7 + 11 \cos \mathrm { t }$
Find the body's velocity at time $t = \pi / 3 \mathrm { sec }$.
A)$- \frac { 11 \sqrt { 3 } } { 2 } \mathrm {~m} / \mathrm { sec }$
B) $\frac { 11 \sqrt { 3 } } { 2 } \mathrm {~m} / \mathrm { sec }$
C) $\frac { 11 } { 2 } \mathrm {~m} / \mathrm { sec }$
D)$ - \frac { 11 } { 2 } \mathrm {~m} / \mathrm { sec }$

Question

Quizplus · Accepted Answer

The velocity is the derivative of the position with respect to time, $v = \frac{ds}{dt}$. For $s = 7 + 11\cos(t)$, $v = -11\sin(t)$. At $t = \pi/3$, $v = -11\sin(\pi/3) = -11\frac{\sqrt{3}}{2}$.

The Equation Gives the Position S = F(t) of a Body